Problem: Factor the following expression: $125x^2 - 45$
Solution: We can start by factoring a ${5}$ out of each term: $ {5}({25x^2} - {9})$ The second term is of the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as ${5}({a} + {b}) ({a} - {b})$ What are the values of $a$ and $b$ $ a = \sqrt{25x^2} = 5x$ $ b = \sqrt{9} = 3$ Use the values we found for $a$ and $b$ to complete the factored expression, ${5}({a} + {b}) ({a} - {b})$ So we can factor the expression as: ${5}({5x} + {3}) ({5x} - {3})$